One thing the astronauts discovered on the moon was that while things like jumping up were pretty straightforward (you just end up jumping about 6 times as high, as was already mentioned), other things weren't so straightforward. Walking, running, and other motions rely on a certain amount of friction between you and the surface you are on, and the moon's reduced gravity reduces the friction as well. So if you try to run, all you end up doing is slipping your feet. As a result, the astronauts found that the easiest way to move across the lunar surface was to bunny hop.

Along with allowing zero-G simulation the 'vomit comet' could alter its parabolic course and instead simulate the 1/6 gravity of the Moon as well. I can't find the footage of it but I've seen film of the Apollo astronauts wearing their lunar surface suits and practicing walking and moving around inside the plane (on a simulated lunar surface) in just this manner.